Lingua franca (on the ground, as opposed to diplomatic French) wasn't exactly French, either; it was a sort of Occitan/Spanish/Italian hybrid that was something more than a mere pidgin (possible because of the common Romance roots of its speakers). The name is more of a "this isn't Italian; sounds like French to me" designation. (William Caxton remarked that London-area English was received similarly in Kent in the 15th century.)